{"id":"https://openalex.org/W2093566764","doi":"https://doi.org/10.1109/tit.1978.1055890","title":"Renyi's entropy and the probability of error","display_name":"Renyi's entropy and the probability of error","publication_year":1978,"publication_date":"1978-05-01","ids":{"openalex":"https://openalex.org/W2093566764","doi":"https://doi.org/10.1109/tit.1978.1055890","mag":"2093566764"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1978.1055890","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055890","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058046689","display_name":"Moshe Ben-Bassat","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["IL","US"],"is_corresponding":true,"raw_author_name":"M. Ben-Bassat","raw_affiliation_strings":["Faculty of Management and Mathematical Sciences Department, Tel-Aviv University, Los Angeles, Israel","University of Southern California, Los Angeles, USA"],"affiliations":[{"raw_affiliation_string":"Faculty of Management and Mathematical Sciences Department, Tel-Aviv University, Los Angeles, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005908822","display_name":"J. Raviv","orcid":null},"institutions":[{"id":"https://openalex.org/I4210167297","display_name":"IBM Research - Haifa","ror":"https://ror.org/05rw9t746","country_code":"IL","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210167297"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"J. Raviv","raw_affiliation_strings":["IBM Israel Scientific Center, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"IBM Israel Scientific Center, Haifa, Israel","institution_ids":["https://openalex.org/I4210167297"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058046689"],"corresponding_institution_ids":["https://openalex.org/I1174212","https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":1.8015,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.85636079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"324","last_page":"331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5479956269264221},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.5452462434768677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5299271941184998},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.482852041721344},{"id":"https://openalex.org/keywords/probability-of-error","display_name":"Probability of error","score":0.46834275126457214},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46696737408638},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4378967583179474},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34773632884025574},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3130652904510498},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2651170492172241},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2639414668083191},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07452186942100525},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05663982033729553}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5479956269264221},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.5452462434768677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5299271941184998},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.482852041721344},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.46834275126457214},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46696737408638},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4378967583179474},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34773632884025574},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3130652904510498},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2651170492172241},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2639414668083191},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07452186942100525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05663982033729553},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1978.1055890","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055890","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W13978628","https://openalex.org/W598560442","https://openalex.org/W1989008275","https://openalex.org/W1995875735","https://openalex.org/W2001935257","https://openalex.org/W2002033577","https://openalex.org/W2009881214","https://openalex.org/W2042587503","https://openalex.org/W2057652230","https://openalex.org/W2074107874","https://openalex.org/W2084790527","https://openalex.org/W2084864772","https://openalex.org/W2122111042","https://openalex.org/W2122882636","https://openalex.org/W2129000925","https://openalex.org/W2149197198","https://openalex.org/W2156642595","https://openalex.org/W2318677045","https://openalex.org/W3028214282","https://openalex.org/W3110683067","https://openalex.org/W4253493393","https://openalex.org/W6678323213"],"related_works":["https://openalex.org/W2011403573","https://openalex.org/W1499116563","https://openalex.org/W1964624186","https://openalex.org/W1574530675","https://openalex.org/W2952645742","https://openalex.org/W3214311941","https://openalex.org/W3196742378","https://openalex.org/W4226485587","https://openalex.org/W2128726013","https://openalex.org/W2113989463"],"abstract_inverted_index":{"The":[0,61],"basic":[1],"properties":[2,11],"of":[3,26,56,73,76],"Renyi's":[4,31],"entropy":[5,32],"are":[6,12,28,34],"reviewed,":[7],"and":[8,33,69],"its":[9],"concavity":[10],"characterized.":[13],"New":[14],"bounds":[15],"(referred":[16],"to":[17],"as":[18],"<tex":[19,48,65],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,49,66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">I_{\\alpha}</tex>":[21],"bounds)":[22],"on":[23],"the":[24,44,47,57,64,70,74],"probability":[25,75],"error":[27,77],"derived":[29],"from":[30],"compared":[35],"with":[36],"known":[37,59],"bounds.":[38,60],"It":[39],"is":[40,52,78],"proved":[41],"that":[42],"for":[43],"two-class":[45],"case,":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">I_{2}</tex>":[50,67],"bound":[51,68],"sharper":[53],"than":[54],"many":[55],"previously":[58],"difference":[62],"between":[63],"real":[71],"value":[72],"at":[79],"most":[80],"0.09.":[81]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
